PROBLEM SOLVING

Nth Term

Learn the reliable method for nth term, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

An nth-term rule gives the value at any position in a sequence.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Find the constant difference for a linear sequence.
  2. Use it as the coefficient of n.
  3. Compare the rule with the first term to find the adjustment, then verify another term.
3 · WORKED EXAMPLES

See the method in action

Example 1

A sequence starts 3, 5, 7 and continues by adding 2 each time. What is term 6?

  1. The first term is 3.
  2. To reach term 6, add 2 a total of 5 times: 3 + 5 × 2 = 13.
Answer: 13
Example 2

A linear sequence has nth term kn+4. Its 10th term is 64 and its 9th term is 58. What is k?

  1. Consecutive terms differ by k.
  2. Their difference is 64−58=6.
Answer: 6
4 · ELEVENSPRINT TIP

A useful shortcut

Compare the rule with the first term to find the adjustment, then verify another term.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.